8/14/2019 Lpw Circuit Theory 2013
1/49
INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY
B.Tech. Semester IV (IC)
2EE225:CIRCUIT THEORY
INDEX
SR.
NO.TITLE
PAGEDATE SIGN
REMAR
KSFROM TO
1. To verify Superposition Theorem.
2. To verify Thevenin Theorem.
3. To verify Reciprocity Theorem.
4. To verify Norton Theorem.
5. To verify Maximum Power Transfer Theorem.
6.
(i) To determine the zparameters of atwo port resistive network.
(ii)To determine the zparameters ofSeries connection of two 2-port resistive
networks and verify the result by direct
calculation.
7.
(i) To determine the y parameters of a twoport resistive network.
(ii) To determine the y parameters of the
parallel connection of two 2-port resistive
networks and verify the result by direct
calculation.
8.
(i) To determine the ABCD parameters of atwo port resistive network.
(ii) To determine the ABCD parameters of the
cascade connection of two 2-port resistive
networks and verify the result by direct
calculation.
9.
(i) To determine the hparameters of a twoport resistive network.
(ii) To determine the h parameters of the
series parallel connection of two 2-port
resistive networks and verify the result by
direct calculation.
10.
(i) To determine the gparameters of a twoport resistive network.
(ii)To determine the g parameters of theparallel-series connection of two 2-port
resistive networks and verify the result by
direct calculation.
11.Simulation of series RC,RL and RLC circuits
with Virtual Laboratory.
12.Simulation of Parallel RC,RL and RLC
circuits with Virtual Laboratory.
8/14/2019 Lpw Circuit Theory 2013
2/49
EXPERIMENT NO: 1 DATE
AIM : To verify Superposition Theorem.
APPARATUS:
(1) Regulated power supply (D.C) 0 - 30V 2
(2) Board containing the network 1
(3) Ammeters 0 - 250 mA 3
(4) Voltmeter 0 - 30 V 1
SUPERPOSITION THEOREM
THEORY:
The superposition theorem states that the response in any element of a linear bilateral
network containing two or more sources is the algebraic sum of the responses obtained by
each source acting separately at a time and with all the other sources set equal to zero,
leaving behind their internal resistance in the network.
According to this theorem, if there are a number of e.m.fs acting simultaneously in any
linear bilateral network, each e.m.f acts independently of the others i.e as if the other
e.m.fs doesn't exist. The value of current in any element of the netwrok is the algebraic
sum of the currents due to each e.m.f. Similarly voltage across any element/branch is the
algebraic sum of the voltages which each e.m.f would have produced while
acting separately at a time. In other words, current through or voltage across
any conductor of the network is obtained by superimposing the currents and voltages
due to each e.m.f. in the network .It is important to note that this theorem is applicable
only to linear networks.
The superposition theorem is applied to determine currents and voltages which are
linearly related to the sources acting on the network. Power can not be determined by
superposition principle since the relationship between power and current or voltage is
quadratic.
In Fig(a) I1, I2and I3represent values of currents due to simultaneous action of the two
sources of e.m.fs in the network. In fig(b) I1', I2' and I' represent values of currents due to
source of e.m.f E1 alone. In fig (c) I1", I2" and I" represent values of currents due to
source of e.m.f E2alone. By superimposing the current values of fig (b) and fig (c)
the actual values of currents due to both the sources can be obtained as under:
8/14/2019 Lpw Circuit Theory 2013
3/49
Obviously : I1= I1' + I1" (algebraic)
I2= I2" + I2' (algebraic)
I = I' + I" (algebraic)
PROCEDURE :
1. Connect the circuit diagram as shown in the fig .2. Connect the network with two e.m.f sources and adjust the source voltages such that
current values are not exceeded beyond the ranges and ratings of the resistance and
note down the meter readings.
3. Set the e.m.f E2 to zero and note down the readings. due to E1 alone. If any meterindicates negative, interchange the connection of that meter and consider that reading
as negative.
4. Adjust E2 as before (as per step. 2) and set E1 to zero and note down the meterreadings If any meter indicates negative, interchange the connection of that meter
and note down the reading of that meter with opposite sign w.r.t. the step 3.
5. Verify the superposition theorem and tabulate the results.
OBSERVATION TABLE:
SR.
NO
E1
Volts
E2
Volts
I1
mA
I2
mA
I3
mA
V1
Volts
V2
Volts
V3
Volts
1
2 0
3 0
CALCULATION:
I1 = I1' + I1" (Algebraic) V1 = V1' + V1" (Algebraic)
I2 = I2' + I2" (Algebraic) V2 = V2' + V2" (Algebraic)
I3 = I3' + I3" (Algebraic) V3 = V3' + V3" (Algebraic)
RESULT TABLE:
SR.
NO
I1
mA
I2
mA
I3
mA
V1
Volts
V2
Volts
V3
Volts
Practical
Theoretical
CONCLUSION:
8/14/2019 Lpw Circuit Theory 2013
4/49
EXPERIMENT NO: 3 DATE
AIM : To verify Reciprocity Theorem.
APPARATUS:
(1) Regulated power supply (D.C) 0 - 30V 2
(2) Board containing the network 1
(3) Ammeters 0 - 250 mA 3
(4) Voltmeter 0 - 30 V 1
RECIPROCITY THEOREM:
THEORY:
The reciprocity theorem states that in a linear, bilateral, single source network the ratio of
excitation to response is constant when the positions of excitation and response are
interchanged.
On the basis of mesh current analysis with a single voltage source acting in the network, the
theorem may be demonstrated by considering the following equation for mesh current Ir.
Ir = V1(1r/z) + V2(2r/z) +.. + Vr(rr/ z) + Vs(sr/ z)
Let the only source in the network be Vsthen
Ir = Vs (sr/ z)
The ratio of excitation to response is
Vs/ Ir= z/ sr= Ztransfer sr ------------------------------(1)
Now when the position excitation and response are interchanged the source becomes Vrand
the current Is.
Is= Vr(rs/ z)
The ratio of excitation to response is
Vr / Is= z/ rs= Ztransfer rs --------------------------(2)
The two transfer impedances in (1) and (2) are equal in any linear, bilateral network since in
such networks the impedance matrix [z] is symmetrical with respect to the principal diagonal,
8/14/2019 Lpw Circuit Theory 2013
5/49
and the cofactors rs and sr are equal. Thus the current in mesh r which results from a
voltage source in mesh s is the same as the current in mesh s when the voltage source is
moves to mesh. It must be noted that currents in other parts of the network will not remain
same.
The reciprocity theorem also applies to networks containing a single current source. Here the
theorem states that the voltage which results at a pair of terminal m n due to a current source
acting at terminals a b is the same as the voltage at terminals a b when the current source is
moved at terminals m n. It should be noted that voltages at other points in the network would
not remain the same.
PROCEDURE:
1. For the circuit shown in figure1 calculate the values of current (I) for different values ofsource voltage and record them in the observation table.
2. Connect the circuit as shown in figure1 , measure then values of current (I) (for sourcevoltage of same values in step 1) and record them in the observation table.
3. For the circuit shown in figure (2), calculate the values of current (I) (for source voltage ofsame values as in step 1) and record them in the observation table.
4. Connect the circuit as shown in figure (2), measure the values of current (I)(for sourcevoltage of same values as in step 1) and record them in the observation table.
OBSERVATION TABLE:
Sr No. Voltage
(V)
Current (I) A/mA Voltage
(V)
Current (I) (A/mA)
Exp. The. Exp. The.
1.
2.
3.
4.
CONCLUSION:
8/14/2019 Lpw Circuit Theory 2013
6/49
QUIZ :
1. Superposition theorem can be applied only to circuits having ________.
2. Superposition theorem requires as many circuits to be solved as there are
(a) sources , nodes and meshes
(b) sources and nodes
(c) sources
(d) nodes.
3. Total resistance of a parallel circuit is _______ the smallest branch resistance.
4. Is superposition theorem applicable to POWER as it is applicable to voltage and current?
8/14/2019 Lpw Circuit Theory 2013
7/49
EXPERIMENT NO: 2 DATE
AIM : To verify Thevenin Theorem.
APPARATUS:
(1) Board containing network 1
(2) Milli ammeter (MC) 0 - 50 mA. 1
(3) Voltmeter (MC) 0 - 10V 1
(4) Regulated power supply 0-30V 1
THEVENIN THEOREM:
THEORY:
Thevenins theorem state that any two terminal network whether simple or complex can
be replaced by a single source of voltage Vth in series with a single resistance Rth (in
case of d.c) or impedance Zth(in case of a.c) Hence Thevenin's equivalent circuit consists
of Vthin series with Rth(or Zth) as shown in fig(B). Once a Thevenin's circuit is obtained
it is connected across the resistance RL in which current is to be determined. Once the
current value in RLis known, potential difference across it can be calculated if required.
For obtaining Thevenin's circuit, proceed as follows:
1. Remove the resistance RL and measure (or calculate) voltage Ethbetween theterminals from where RL has been removed.
2. Replace all the e.m.f sources by their internal resistance (or impedances) andmeasure (or calculate) Rth (or Zth) between the terminals from where RL has been
disconnected.
3. Draw the Thevenin's equivalent network.4. For calculating current in RL, connect RL which was removed earlier across this
Thevenin's circuit.
5. Current through RLis given byVth
IL = -----------
Rth+ RL
8/14/2019 Lpw Circuit Theory 2013
8/49
PROCEDURE:
1. Connect the circuit as shown in the fig(1).2. Switch on the supply and adjust the supply voltage such that meter readings are not
exceeded their ranges and ratings of the resistances. Note down the current through the
load resistance RL.
3. Disconnect the resistance RL from the circuit and measure the voltage across theterminals from where the resistance RL is disconnected. This voltage is known as Eth.
Refer fig(2).
4. Replace source of e.m.f. by its internal resistance and measure the total resistance (orimpedance) of the network between the terminals from where the resistance RL is
disconnected. This resistance (or impedance) is known as Rth(or Zth). Refer fig(3).
5. Calculate the current through RLusing the formula.Vth
IL = -----------
Rth + RL
6. Compare it with the value obtained in step (2)
OBSERVATION TABLE:
SR.
NO
VOLTAGE
ACROSS
RL
VLvolts
CURRENT
THROUGH
RL
ILmA
RL=
VL/IL
Eth
Volts
REMARKS
1
2- - Disconnect the
resistance RL
(Measurement of Rth)
SR
NO
SUPPLY
VOLTAGE
V volts
CURRENT
I mA
Rth=
V / I
REMARKS
1 Set source e.m.f to zero
2 Set source e.m.f to zero
8/14/2019 Lpw Circuit Theory 2013
9/49
CALCULATION :
(1) RL= VL/IL = =
(2) Rth= V/I = =
Vth
(3) IL = ----------- = =
Rth + RL
RESULT TABLE :
THEORETICAL PRACTICAL
Vth
Rth
IL
CONCLUSION:
8/14/2019 Lpw Circuit Theory 2013
10/49
EXPERIMENT NO: 4 DATE
AIM : To verify Norton Theorem.
APPARATUS:
(1) Board containing network 1
(2) Milli ammeter (MC) 0 - 50 mA. 1
(3) Voltmeter (MC) 0 - 10V 1
(4) Regulated power supply 0-30V 1
NORTON THEOREM:
THEORY :
This theorem is an alternative to the Thevenin's theorem. In fact, it is the dual of
Thevenin's theorem. Where as Thevenin's theorem reduces a two - terminal active
network to an equivalent constant voltage source and series resistance Norton's theorem
replaces the network by an equivalent constant current source and a parallel resistance.
It states that any two - terminal active network containing voltage/current sources and
resistances/impedances when viewed from its output terminals is equivalent to a
constant current source and a parallel resistance (or impedance). The constant current is
equal to the current which would flow in a short - circuit placed across the terminals
and parallel resistance (or impedance) is the resistance (or impedance) of the network
when viewed from these open circuited terminals after all sources of e.m.fs have been
supressed and replaced by their internal resistances (or impedances).
PROCEDURE for analysis of network:
1. Remove the resistance RL, short the terminals through an ammeter from where RLhas been removed and observe ( or calculate) the reading of the ammeter. This gives
the value of the current of the Nortons current source, Isc.
2. Replace the source by its internal resistance (or impedance) and measure (orcalculate) the resistance RN(or impedance ZN) between the terminals from where RL
has been removed.
3. Connect the RN(or ZN) in parallel with the current source and connect RL whichwas disconnected earlier across Norton's equivalent circuit.
4. Current through the resistance RL is given byRth
IL = Isc ----------Rth+ RL
8/14/2019 Lpw Circuit Theory 2013
11/49
PROCEDURE:
1. Connect the circuit as shown in fig 1.2. Switch on the power supply and adjust the supply voltage such that meter readings
are not exceeded their ranges and ratings of the resistances. Note down the current
through the resistance RL.
3. Disconnect the resistance RL and short the terminals through the ammeter fromwhere RLhas been removed and measure(or calculate) the current. This gives the
value of the current (Isc) of the current source. Refer fig(2).
4. Replace source of e.m.f by its internal resistance (or impedance) and measure the totalresistance (or impedance) of the network between the terminals from where the
resistance(RL) has been removed. This is known as RN(or ZN).
5. Calculate the current through RL according toRN
IL = Isc -----------
RN+ RL
and compare its value obtained in step (2)
OBSERVATION TABLE:
SR.
NO
VOLTAGE
ACROSSRL
VLvolts
CURRENT
THROUGHRL
ILmA
RL=
VL/IL
ISC
mA
REMARKS
1 -
2 Disconnect RL and
short the terminals
through ammeter
8/14/2019 Lpw Circuit Theory 2013
12/49
(Measurement of RN)
SR.
NO
SUPPLY
VOLTAGE
V volts
CURRENT
I mA
RN= V / I REMARKS
1 Set source e.m.f. to zero
2 Set source e.m.f. to zero
CALCULATION :
(1) RL= VL/IL = =
(2) RN= V/I = =
RN
(3) IL = Isc ----------- = =
RN+ RL
RESULT TABLE:
THEORETICAL PRACTICAL
ISC
RN
IL
CONCLUSION: -
QUIZ: -
1. For which type of network the Norton's theorem is applicable?2. The circuit whose parameters change with voltage or current is called a _______ circuit.
3. _________ theorem is quite useful when the current in one branch of a network is to be
determined or when the current in an added branch is to be calculated.
8/14/2019 Lpw Circuit Theory 2013
13/49
4.. The circuit whose parameters are constant is called a linear circuit. (yes/no)
5. In Thevenin's theorem to find Zth,all independent ________ are set to zero and allindependent_______ are open circuited.
6. Thevenin equivalent circuit is preferred when the circuit is analyzed in terms of _________and __________ .
7. Norton equivalent circuit is preferred when the circuit is analyzed in terms of _________ and__________ .
8. When connected to a 4 resistor, a battery has a terminal voltage of 10.8 V but produces 12V on an open circuit. Determine the Thevenin equivalent circuit for the battery.
9. Given the Thevenin`s equivalent of an electric circuit, how will you determine the Norton`sequivalent?
.
8/14/2019 Lpw Circuit Theory 2013
14/49
EXPERIMENT NO: 5 DATE
AIM: To verify Maximum Power Transfer Theorem and Tellegan`s Theorem.
APPARATUS:
(1) Board
(2) Ammeter 0 - 10 ma 01
(3) Voltmeter 0 - 10V 01
(4) Regulated power supply 0-30V 01
MAXIMUM POWER TRANSFER THEOREM
THEORY :
Maximum power transfer theorem deals with transfer of maximum power from a
source to load. This theorem in d.c circuit states the relationship between the load
resistance and the internal resistance of the source for maximum power transfer from
source to load. This condition is also referred as resistance matching and it is
very important in electronics and communication circuits for obtaining maximum
output. Let us consider a circuit supplying a power to a load of resistance RL ohms.
The circuit of fig (1) can be simplified to the circuit of fig (2) by using Thevenin's
theorem, From fig (2) the current through RL is given by
E
I = -------Ri + RL
Power transferred to the load
PL= I2RL
E 2
= -------- RL
Ri + RL
E2
RL= ----------- -----------(1)
(Ri + RL)2
In the above expression the resistance Rs and voltage E are constant. Hence PL varies
wth respect to only variable RL Power delivered to the load is a maximum if,
d PL
------ = 0
d RL
8/14/2019 Lpw Circuit Theory 2013
15/49
Differentiating the expression (1) w.r.to RL and equating to zero, we obtain the
condition for maximum power i.e RL = Ri
Hence for maximum power transfer the load resistance should be equal to the internal
resistance of the source,
E2RL
Pmax = ------------
(RL+ Ri)
2
E2
= ------- watts (because RL= Ri)
4RL
PROCEDURE:
(1)Connect the circuit as shown in the fig.(3)(2)Switch on the supply and adjust suitable voltage of the supply.(3)Vary the load resistance from zero onward in suitable steps. For each step take meter
readings.
(4)Calculate the power taken by the load for each value of the load resistance.(5)Draw the graph of PLv/s RL.
OBSERVATION TABLE :
SR.
NO
SUPPLY
VOLTAGE
Vs (Volts)
LOAD
CURRENT
IL( mA)
VOLTAGE
ACROSS
LOADVL(Volts)
LOAD
RESISTANCE
RL= VL/IL
POWER
DELIVERED TO
THERESISTANCE,
RL
PL= IL2XRL
1.2.3.4.5.
CALCUATION :
VL
(1) RL= -----
IL
(2) PL= IL2. RL
8/14/2019 Lpw Circuit Theory 2013
16/49
CONCLUSION: -
QUIZ: -
1. When a source is delivering maximum power to a load, the efficiency of the circuit is___________ .
2. Assuming that we can determine the Thevenin equivalent resistance of our wall socket,why don`t heater, microwave oven and TV manufacturer match each appliances
Thevenin equivalent resistance of this value? Would not is permited max power transfer
from the utility company to our household appliances?
3. A black box with a circuit in it is connected to a variable resistor. An ideal ammeter andan ideal voltmeter are used to measure current and voltage respectively. The results are:
R V I
2 3 1.5 Determine the maximum power from the box.
8 8 1.0
14 10.5 0.75
4. Maximum power transfer theorem is particularly useful for analyzing _________networks.
5. For high efficiency of transfer of power, internal resistance of the source should be__________.
8/14/2019 Lpw Circuit Theory 2013
17/49
EXPERIMENT NO: 6 DATE
AIM : (i) To determine z parameters of a given TwoPort Resistive
Network.
(ii) To determine the z parameters of series connection of two 2-port
resistive networks and verify the result by direct calculation.
APPARATUS :
(1) Ammeter 0-50mA 2
(2) Voltmeter 0-10V 1
(3) Regulated power supply 0 - 30V. 1
(4) Board containing two port network 1
THEORY:
In electrical network theory a port may be regarded as a pair of terminals in which
current in to one terminal equals the current out of the other. A network may have one,
two or n ports in general. A one port network is completely identified when voltage
current relationship at the terminals of the port is given.
A general two port network shown in fig (1) has two pairs of voltage - current
relationships. The V1 and I1 are the variables at port 1 and V2 and I2 are the variables
at port 2. Only two of the four variables are independent and specifications of any two
of them determine the remaining two. The dependence of two of the four variables on
the other two is described in a number of ways, depending on which of the variables
are chosen to be independent variables. As such there are six possible sets of equations
describing a two port network, six different types of parameters are defined as z
parameters, y parameters, transmission parameters, inverse transmission parameters,
hybrid parameters and inverse hybrid parameters.
Z - parameters:
In case of z parameters, V1and V2are expressed in terms of I1 and I2.
i.e. V1= z11I1 + z12I2 - (1)
V2= z21I1+ z22I2 - (2)
These parameters may be defined in terms of a single voltage and current by letting either
I1= 0 or I2= 0.
Thus,
8/14/2019 Lpw Circuit Theory 2013
18/49
V1
z11 = ___
I1 I2= 0
V1
z12 = ___
I2 I1= 0
V2
z21 = ___
I1 I2= 0
V2
z22 = ____
I2 I1= 0
It may be observed that (i) all the z parameters have the dimensions
of impedance and (ii) they are specified only when the current in one of ports is
zero i.e open circuit at port 1 or port 2. Hence z parameters are designated as
open circuit impedance parameters.
ZPARAMETERS OF SERIES CONNECTION OF TWO 2-PORT
RESISTIVE NETWORK:
Two port network analysis is useful for finding different parameters. The z
Parameters are useful in characterizing series connected two port networks. They
are found under open circuit conditions and hence they are referred as open circuit
impedance functions. They are defined and found as under:
The z parameters are useful in characterizing series connected two port
networks. The overall z parameters from the individual z parameters can be
found as under when the networks are connected in series.
For network Na
V1a
=
z11a z12a I1a
V2a z21a z22a I2a ---------(1)
8/14/2019 Lpw Circuit Theory 2013
19/49
For network Nb
V1b
=
z11b z12b I1b
V2b z21b z22b I2b ---------(2)
For overall network N
V1
=
z11 z12 I1
V2 z21 z22 I2 ---------(3)
Note that
I1= I1a= I1band V1= V1a+ V1b
I2= I2a= I2band V2= V2a+ V2b------(4)
Combining equation (1), (2) and (4), we get
V1
=
Z11a+z11b z12a +z12b I1
V2 Z21a+z21b z22a +z22b I2 ---------(5)
Comparing equation (5) with equation (3), we get
z11= z11a + z11b
z12= z12a + z12b
z21= z21a + z21b
z22= z22a + z22b----------------(6)
This result may be generalized for any number of networks
connected in series. The individual parameters are added to determine the
overall Z parameters.
PROCEDURE :
(1) Connect the circuit for Network Naas shown in fig (1).
(2) Apply voltage at port 1 keeping port 2 open circuited as shown in
fig (2). Measure voltages and current at the port terminals. Keep levels of voltages
and current such that meter readings are not exceeded their ranges and ratings of
the resistances.
(3) Apply voltage at port 2 keeping port 1 open circuited as shown in
fig (3). Measure voltages and current at the port terminals.
8/14/2019 Lpw Circuit Theory 2013
20/49
(1)Calculate z parameters using measured values of voltages and currentsand verify the results theoretically.
(2)Connect the circuit as shown in fig (4) for network Nb only. Repeat steps 2 to4 for Network Nb
(6) Connect the networks Na and Nb in series as shown in fig(5) to form
the overall network N.
(7) Repeat steps 2 to 4 to find the z - parameters of network N and Verify the
results theoretically.
(8) Keep levels of voltages and currents such that the meter readings are
not exceeded their ranges and ratings of resistances.
OBSERVATION TABLE :
(1) Network : Na
SR.
NO.
V1a
Volts
I1a
mA
V2a
Volts
I2a
mA
REMARK
1 0 Port - 2 open circuited
2 0 Port - 1 open circuited
(2) Network : Nb
SR.
NO.
V1b
Volts
I1b
mA
V2b
Volts
I2b
mA
REMARK
1 0 Port - 2 open circuited
2 0 Port - 1 open circuited
(3) Network N :
SR.
NO.
V1
Volts
I1
mA
V2
Volts
I2
mA
REMARK
1 0 Port - 2 open circuited
2 0 Port - 1 open circuited
8/14/2019 Lpw Circuit Theory 2013
21/49
CALCULATION :
For Network Na :
V1a
z11a = ___ = _________________________________
I1a I2a= 0
V1a
z12a = ___ = _________________________________
I2a I1a = 0
V2a
z21a = ___ = ________________________________
I1a I2a= 0
V2a
z22a = ___ = ________________________________
I2a I1a= 0
For Network Nb :
V1b
z11b = ___ = _________________________________
I1b I2b= 0
V1b
z12b = ___ = _________________________________
I2b I1b= 0
V2b
z21b = ___ = ________________________________
I1b I2b= 0
V2b
z22b = ___ = ________________________________
I2b I1b= 0
8/14/2019 Lpw Circuit Theory 2013
22/49
For Network N :
V1
z11 = ___ = _________________________________
I1 I2= 0
V1
z12 = ___ = _________________________________
I2 I1= 0
V2
z21 = ___ = ________________________________
I1 I2= 0
V2
z22 = ___ = ________________________________
I2 I1= 0
Check :
(1) z11= z11a+ z11b = ____________ = ____________
(2) z12= z12a+ z12b = ____________ = ____________
(3) z21= z21a+ z21b=____________ = ____________
(4) z22= z22a+ z22b = ____________ = ____________
RESULT TABLE :
NETWORK Practical Theoratical
Network Na
z11a=______ z21a= ______
z11a=______ z21a= ______
z11a=______ z21a= ______
z11a=______ z21a= ______
z11b =______ z21b = ______ z11b=______ z21b= ______
8/14/2019 Lpw Circuit Theory 2013
23/49
Network Nb
z11b=______ z21b= ______ z11b=______ z21b= ______
Network N
z11=______ z21= ______
z11=______ z21= ______
z11=______ z21= ______
z11=______ z21= ______
CONCLUSION: -
QUIZ: -
1. What do you mean by two port network?2. z parameters are known as _________ circuit parameters.3. If for any two port passive network z12is 4 ohm, what will be the value of z21?4. What are the applications of two port parameters?5. Why two networks are connected in series to get overall z parameters?6. For two networks connected in series if z21 a= 4 ohm and z21b= 6 ohm , what will
be the value of z21 ?
8/14/2019 Lpw Circuit Theory 2013
24/49
EXPERIMENT NO: 7 DATE
AIM : (i) To determine y parameters of a given TwoPort Resistive
Network.
(ii) To determine the y parameters of the parallel connection of two
2-port resistive networks and verify the result by direct
calculation.
APPARATUS :
(1) Ammeter 0-50mA 2
(2) Voltmeter 0-10V 1
(3) Regulated power supply 0 - 30V. 1
(4) Board containing two port network 1
THEORY:
y parameters :
In case of y parameters , I1 and I2 are expressed in terms of V1 and V2
i.e I1 = y11V1 + y12V2
I2 = y21V1 + y22V2
The individual y parameters are defined by
I1
y11 = ___
V1 V2= 0
I1
y12 = ___
V2 V1= 0
I2
y21 = ____
V1 V2 = 0
I2
y22 = ___
V2 V1= 0
It may be observed that
(i) All the y-parameters have the dimensions of admittance.
(ii) They are specified only when voltage at one of the ports is zero i.e short
circuit at port 1 or port 2. Hence y parameters are known as short circuit
admittance parameters.
8/14/2019 Lpw Circuit Theory 2013
25/49
YPARAMETERS OF PARALLEL CONNECTION OF TWO 2- PORT
RESISTIVE NETWORK.
The y - parameters ( short - circuit admittance parameters ) are useful in
characterizing parallel connected two - port networks.
They are found under short circuit conditions and hence they are referred
as short circuit admittance parameters.
The y-parameters are useful in characterizing parallel connected two port
networks. The overall y parameters from the individually parameters can be
found as under when the networks are connected in parallel.
For network Na
I1a y11a y12a V1a
I2a
=
y21a y22a V2a
---------(1)
For network Nb
I1b y11b y12b V1b
I2b
=
y21b y22b V2b
---------(2)
For overall network N
I1 y11 y12 V1
I2
=
y21 y22 V2
---------(3)
Note that
V1= V1a= V1band I1= I1a+ I1b
V2= V2a= V2band I2= I2a+ I2b------(4)
Combining equation (1), (2) and (4), we get
I1 y11a+y11b y12a +y12b V1
I2
=
y21a+y21b y22a +y22b V2
---------(5)
8/14/2019 Lpw Circuit Theory 2013
26/49
Comparing equation (5) with equation (3), we get
y11= y11a + y11b
y12= y12a + y12b
y21= y21a + y21b
y22= y22a + y22b----------------(6)
This result may be generalised for any number of networks connected
in parallel. The individual short circuit admittance parameters are added to
determine the overall Y parameters.
PROCEDURE :
(1)Connect the circuit diagram of Network Na as shown in fig(1).(2)Apply voltage at port 1 short circuiting the port 2 through
an ammeter as shone in fig (2). Measure voltage and currents at both
the port terminals.
(3)Apply voltage at port 2 short circuiting the port 1 throughan ammeter as shown in fig (3). Measure voltage and currents at both
the ports.
(4)Calculate y parameters using measured values of voltageand currents and verify the results theoretically.
(5)Connect the circuit as shown in fig (4) for network Nb only. Repeatsteps 2 to 4 for Network Nb.
(6)Connect the networks Na and Nb in parallel as shown in fig(5)to form network N and repeat steps 2 to 4 for Network N. find its
y - parameters. Verify the results theoretically.
(7)Keep levels of voltages and currents such that the meterreadings are not exceeded their ranges and ratings of resistances
OBSERVATION TABLE :
(1) Network : Na
SR.
NO.
V1a
VOLTS
I1a
mA
V2a
VOLTS
I2a
mA
REMARK
1 0 Port - 2 short circuited
2 0 Port - 1 short circuited
8/14/2019 Lpw Circuit Theory 2013
27/49
(2) Network : Nb
SR.
NO.
V1b
VOLTS
I1b
mA
V2b
VOLTS
I2b
mA
REMARK
1 0 Port - 2 short circuited
2 0 Port - 1 short circuited
(3) Network N :
SR.
NO.
V1
VOLTS
I1
mA
V2
VOLTS
I2
mA
REMARK
1 0 Port - 2 short circuited
2 0 Port - 1 short circuited
CALCULATION :
For Network Na :
I1a
y11a = ___ = ________________________________
V1a V2a= 0
I1a
y12a = ___ = ________________________________
V2a V1a= 0
I2a
y21a = ___ = _________________________________
V1a V2a= 0
I2a
y22a = ___ = ________________________________
V2a V1a= 0
For Network Nb :
I1b
y11b = __ = _________________________________
V1b V2b= 0
8/14/2019 Lpw Circuit Theory 2013
28/49
I1b
y12b = ___ = _________________________________
V2b V1b= 0
I2b
y21b = ___ = _________________________________
V1b V2b= 0
I2b
y22b = ___ = ________________________________
V2b V1b= 0
For Network N :
I1
y11 = ___ = ________________________________
V1 V2= 0
I1
y12 = ___ = ________________________________
V2 V1= 0
I2
y21 = ___ = _________________________________
V1 V2= 0
I2
y22 = ___ = ________________________________
V2 V1= 0
Check :
(1) y11= y11a+ y11b = ____________ = ____________
(2) y12= y12a+ y12b = ____________ = ____________
(3) y21= y21a+ y21b =____________ = ____________
(4) y22= y22a+ y22b = ____________ = ____________
8/14/2019 Lpw Circuit Theory 2013
29/49
RESULT TABLE :
NETWORK Practical Theoretical
Network Nay11a=______ y21a= ______
y11a=______ y21a= ______
y11a=______ y21a= ______
y11a=______ y21a= ______
Network Nb
y11b =______ y21b = ______
y11b=______ y21b= ______
y11b=______ y21b= ______
y11b=______ y21b= ______
Network N
y11=______ y21= ______
y11=______ y21= ______
y11=______ y21= ______
y11=______ y21= ______
CONCLUSION: -
QUIZ: -
1. y parameters are also known as _______ circuit parameters.2. If for any two port passive network y12is 0.4 mho, y21= ______.3. If two networks Naand Nbare connected in parallel y11a= 3 mho and y11b= 4 mho
what will be the value of y11= ______.
8/14/2019 Lpw Circuit Theory 2013
30/49
EXPERIMENT NO: 8 DATE
AIM : (i) To determine ABCD parameters of a given twoport resistive
network.
(ii) To determine the ABCD parameters of the cascade connection of
two 2-port resistive networks and verify the result by direct
calculation.
APPARATUS :
(1) Network board
(2) Ammeters 0 - 50mA 2
(3) Voltmeter 0 - 10V 1
(4) Regulated power supply 0-30 V 1
THEORY :
The transmission parameters serve to relate the voltage and current at one port to
voltage and current at the other port. In equation form,
V1 = AV2 - BI2
I1 = CV2 - DI2
where A, B, C and D are the transmission parameters. They are also known
as chain parameters, the ABCD parameters and general circuit parameters.
Their first use is in the analysis of power transmission lines. From the
circuit conditions, they can be found as follows,
V1
A = _____
V2 I1=0
V1
-B = _____
I2 V2=0I1
C = _____
V2 I2=0
I1
-D = _____
I2 V2=0
8/14/2019 Lpw Circuit Theory 2013
31/49
ABCD PARAMETERS OF CASCADE CONNECTION OF TWO 2-PORT
RESISTIVE NETWORK.
The transmission parameters are useful in describing two port networks which
are connected in cascade or in a chain arrangement. The overall parameters
from the individual parameters can be found as under when the networks are
connected in cascade.
For network Na
V1a Aa Ba V2a
I1a= Ca Da -I2a
---------(1)
For network Nb
V1b Ab Bb V2b
I1b
=
Cb Db -I2b
---------(2)
For overall network N
V1 A B V2
I1
=
C D -I2
---------(3)
Note that
V1a= V1 V2a = V1b I2b= I2
I1a = I1 I1b = - I2a V2b = V2 ------(4)
Substituting these in equation (1) and equation (2), we get
V1 Aa Ba Ab Bb V2
I1
=
Ca Da Cb Db -I2
---------(5)
Comparing equation (5) with equation (3), we get
A B Aa Ba Ab Bb AaAb+BaCb AaBb+ BaDb
C D=
Ca Da Cb Db=
CaAb+ DaCb CaBb+ DaDb------(6)
8/14/2019 Lpw Circuit Theory 2013
32/49
PROCEDURE :
(1)Connect circuit diagram of Network Naas shown in fig (1).(2)Apply voltage at port 1 of network Na short circuiting the port
2 through an ammeter as shown in fig (4). Measure voltages and
currents at both the ports.
(3)Apply voltage at port 1 of network Na keeping port 2 open circuited asshown in fig (5). Measure voltages and currents at both the ports.
(4)Calculate ABCD parameters using measured values of voltagesand currents.
(5)Connect the circuit as shown in fig (2) for network Nb only. Repeatsteps 2 to 4 for network Nb.
(6)Connect both the networks in cascade as shown in fig (3). This formsnetwork N.
(7)To measure parameters of network N follow the steps 2 to 4.(8)Verify the parameters theoretically and tabulate the results.(9)For each network verify that AD - BC = 1.
OBSERVATION TABLE :
(1) Network : Na
SR.
NO.
V1a
Volts
I1a
mA
V2a
Volts
I2a
mA
REMARK
1 0 Port - 2 short circuited
2 0 Port - 2 open circuited
(2) Network : Nb
SR.
NO.
V1b
Volts
I1b
mA
V2b
Volts
I2b
mA
REMARK
1 0 Port - 2 short circuited
2 0 Port - 2 open circuited
8/14/2019 Lpw Circuit Theory 2013
33/49
(3) Network N :
SR.
NO.
V1
Volts
I1
mA
V2
Volts
I2
mA
REMARK
1 0 Port - 2 short circuited2 0 Port - 2 open circuited
CALCULATION :
For Network Na :
V1a
Aa = ___ = _________________________________
V2a I2a= 0
V1a
Ba = ___ = _________________________________
-I2a V2a= 0
I1a
Ca = ___ = _______________________________
V2a I2a= 0
I1a
Da = ___ = _______________________________
-I2a V2a= 0
For Network Nb :
V1b
Ab = ___ = _________________________________
V2b I2b= 0
V1b
Bb = ___ = _________________________________
-I2b V2b= 0
8/14/2019 Lpw Circuit Theory 2013
34/49
I1b
Cb = ___ = _______________________________
V2b I2b= 0
I1b
Db = ___ = ________________________________
-I2b V2b= 0
For Network N :
V1
A = ___ = _________________________________
V2 I2= 0
V1
B = ___ = _________________________________
-I2 V2= 0
I1
C = ___ = ________________________________
V2 I2= 0
I1
D = ___ = ________________________________
-I2 V2= 0
Check :
A = AaAb+BaCb =_________________
B = AaBb+ BaDb =_________________
C = CaAb+ DaCb =_________________
D = CaBb+ DaDb =_________________
8/14/2019 Lpw Circuit Theory 2013
35/49
RESULT TABLE :
NETWORK - Na NETWORK - Nb NETWORK - N
Pract. Theo. Pract. Theo. Pract. Theo.
Aa Ab ABa Bb B
Ca Cb C
Da Db D
CONCLUSION :
QUIZ :
1. ABCD parameters are also known as ___________ or _________ parameters.2. Why two networks are connected in cascade connection to get overall ABCD
parameter?
3. If A= 7 , B= 8 ohm and C = 2.5 mho , what will be the value of D?
4. Ratio of driving voltage in one mesh to resulting current in other mesh is knownas ________ impedance.
5. State the conditions for a network to be loss less in terms of ABCD parameters?6. State the condition for a network to be reciprocal and symmetrical.7. For _________ connection of two 2-port networks, ABCD parameters have to be
multiplied.
8. Are the ABCD parameters A(s), B(s),C(s) and D(s) the network functions?9. The relation ADBC = 1 is valid for ________ and _________ networks.10.Why negative sign is introduced in the equations?
8/14/2019 Lpw Circuit Theory 2013
36/49
EXPERIMENT NO: 9 DATE
AIM : (i) To determine h - parameter of a given TwoPort Resistive
Network.
(ii) To determine the hparameters of the series parallel
connection of two 2-port resistive networks and verify the result
by direct calculation.
APPARATUS :
(1) Network board
(2) Ammeters 0 - 50mA 2
(3) Voltmeter 0 - 10V 1
(4) Regulated power supply 0-30 V 1
THEORY :
h parameters representation is widely used in modeling of electronic
components and circuits, particularly transistors. As both short circuit
and open circuit terminal conditions are utilized hence, this parameter
representation is known as hybrid parameter representation. In this form
of representation, the voltage of the input poet and the current of the
output port are expressed in terms of the current of the input poet and the
voltage of the output port.
We know that
V1= h11I1 + h12V2
I2= h21I1+ h22V2
In matrix form
V1 h11 h12 I1
I2=
h21 h22 V2---------(1)
Where
V1
h11 = ___ = Input impedance when output is short circuited
I1 V2= 0
V1
h12
= ___ = Reverse voltage ratio when input open circuited
V2 I1= 0
8/14/2019 Lpw Circuit Theory 2013
37/49
I2
h21 = ___ = Forward current ratio when output short circuited
I1 V2= 0
I2
h22 = ___ = Output admittance when input is open circuited
V2 I1= 0
h PARAMETERS FOR SERIES PARALLEL CONNECTION OF
TWO 2-PORT NETWORK.
Two port networks are said to be connected in series-parallel if the input
ports are connected in series while the output ports are connected inparallel.
For network Na
V1a h11a h12a I1a
I2a
=
h21a h22a V2a
---------(2)
For network Nb
V1b h11b h12b I1b
I2b
=
h21b h22b V2b
---------(3)
For overall network Nc
V1 h11 h12 I1
I2
=
h21 h22 V2
---------(4)
Note that
I1= I1a= I1band V1= V1a+ V1b
I2= I2a+ I2band V2= V2a= V2b------(4)
Combining equation (2), (3) and (4), we get
V1 h11a+h11b h12a +h12b I1
I2
=
h21a+h21b h22a +h22b V2
---------(5)
8/14/2019 Lpw Circuit Theory 2013
38/49
Comparing equation (5) with equation (3), we get
h11= h11a+h11b
h12= h12a +h12b
h21= h21a+h21b
h22= h22a +h22b----------------(6)
This result may be generalized for any number of networks
connected in series-parallel. The overall h-parameter matrix for series-
parallel connected two port networks is simply the sum of h-parameter
matrices of each individual two-port network connected in series-parallel.
PROCEDURE :
(1)Connect the circuit diagram of network Naas shown in fig (1).(2)Apply voltage at port 1 keeping port 2 short-circuited. Measure
voltages and current at the port terminals as shown in fig (4). Keep
levels of voltages and current such that meter readings are not
exceeded their ranges and ratings of the resistances.
(3)Apply voltage at port 2 keeping port 1 open circuited as shown in fig(5). Measure voltages and current at the port terminals.
(4)Calculate h parameters using measured values of voltagesand currents and verify the results theoretically
(5)Connect the circuit as shown in fig (2) for network Nb only. Repeatsteps 1 to 4 for network Nb.
(6)Connect the networks Naand Nbin series parellel as shown in fig (3) toform the network N.
(7)Repeat steps 2 to 4 to find h parameter for network N and verify resultstheoretically.
(8)Keep levels of voltages and currents such that the meterreadings are not exceeded their ranges and ratings of resistances
8/14/2019 Lpw Circuit Theory 2013
39/49
OBSERVATION TABLE :
(1) Network : Na
SR.
NO.
V1a
Volts
I1a
mA
V2a
Volts
I2a
mA
REMARK
1 0 Port - 2 short circuited
2 0 Port - 1 open circuited
(2) Network : Nb
SR.
NO.
V1b
Volts
I1b
mA
V2b
Volts
I2b
mA
REMARK
1 0 Port - 2 short circuited
2 0 Port - 1 open circuited
(3) Network N :
SR.
NO.
V1
Volts
I1
mA
V2
Volts
I2
mA
REMARK
1 0 Port - 2 short circuited
2 0 Port - 1 open circuited
CALCULATION :
For Network Na :
V1a
h11a = ___ =
I1a V2a= 0
V1a
h12a = ___ =
V2a I1= 0
8/14/2019 Lpw Circuit Theory 2013
40/49
I2a
h21a = ___ =
I1a V2a= 0
I2a
h22a = ___ =
V2a I1a= 0
For Network Nb :
V1b
h11b = ___ =
I1b V2b= 0
V1b
h12b = ___ =
V2b I1= 0
I2b
h21b = ___ =
I1b V2b= 0
I2b
h22b = ___ =
V2b I1b= 0
8/14/2019 Lpw Circuit Theory 2013
41/49
For Network N :
V1
h11 = ___ =
I1 V2= 0
V1
h12 = ___ =
V2 I1= 0
I2
h21 = ___ =
I1 V2= 0
I2
h22 = ___ =
V2 I1= 0
Check :
(1) h11= h11a+h11b = ____________= ____________
(2) h12= h12a +h12b = ____________= ____________
(3) h21= h21a+h21b =____________ = ____________
(4) h21= h21a+h21b= ____________ = ____________
CONCLUSION: -
8/14/2019 Lpw Circuit Theory 2013
42/49
EXPERIMENT NO: 10 DATE
AIM : (i) To determine g - parameter of a given TwoPort Resistive
Network.
(ii) To determine the g parameters of the parallel-series
connection of two 2-port resistive networks and verify the result
by direct calculation.
APPARATUS :
(1) Network board
(2) Ammeters 0 - 50mA 2
(3) Voltmeter 0 - 10V 1
(4) Regulated power supply 0-30 V 1
THEORY :
Hybrid parameters (h parameters) and Inverse hybrid parameters (g parameters) are
dual of each other. For g parameters both short circuit and open circuit terminal
conditions are utilized. In this form of representation, the current of the input port and
the voltage of the output port are expressed in terms of the voltage of the input port
and the current of the output port.
In case of g parameters, I1and V2are expressed in terms of V1 and I2.
i.e. I1= g11V1 + g12I2 - (1)
V2= g21V1+ g22I2 - (2)
I1 g11 g12 V1
V2=
g21 g22 I2---------(1)
Where
I1
g11 = ___ = Input admittance when output is open circuited
V1 I2= 0
g12 = I1 = Reverse current ratio when input short circuited
I2 V1= 0
8/14/2019 Lpw Circuit Theory 2013
43/49
V2
g21 = ___ = Forward voltage ratio when output open circuited
V1 I2= 0
V2
g22 = ___ = Output impedance when input is short circuited
I2 V1= 0
PARAMETERS FOR PARALLEL - SERIES CONNECTION OF TWO 2-PORT
RESISTIVE NETWORK
Two port networks are said to be connected in parallel series if the input ports are
connected in parallel while the output ports are connected in series.
For network Na
I1a g11a g12a V1a
V2a
=
g21a g22a I2a
---------(2)
For network Nb
I1b g11b g12b V1b
V2b
=
g21b g22b I2b
---------(3)
For overall network Nc
I1 g11 g12 V1
V2
=
g21 g22 I2
---------(4)
8/14/2019 Lpw Circuit Theory 2013
44/49
Note that
I1= I1a+ I1band V1= V1a= V1b
I2= I2a= I2band V2= V2a+ V2b------(5)
Combining equation (2), (3) and (5), we get
I1 g11a+g11b g12a +g12b V1
V2
=
g21a+g21b g22a +g22b I2
---------(6)
Comparing equation (6) with equation (4), we get
g11= g11a+g11b
g12= g12a +g12b
g21= g21a+g21b
g22= g22a +g22b----------------(6)
This result may be generalized for any number of networks connected in parallel-series.
The overall g-parameter matrix for parallel-series connected two port networks is simply
the sum of g-parameter matrices of each individual two-port network connected in
parallel-series.
PROCEDURE :
(1)Connect the circuit diagram of network Naas shown in fig (1).(2)Open the output port and excite the input port with a known voltage
source Vs as shown in fig (2) so that V1= Vs and I2= 0.
(3)Determine I1and V2to obtain g11and g21.(4)Then the input port is short circuited and output port is excited with the
same voltage source Vs as shown in fig (3) so that V2= Vs and V1= 0.(5)Determine I1and I2to obtain g12and g22.(6)Connect the circuit as shown in fig (4) for network Nb only. Repeat
steps 2 to 4 for network Nb.
(7)Connect the networks Na and Nb in parallel-series as shown in fig (5) toform the network N.
(8)Repeat steps 2 to 4 for Network N and verify results theoretically.(9)Keep levels of voltages and currents such that the meter
readings are not exceeded their ranges and ratings of resistances
8/14/2019 Lpw Circuit Theory 2013
45/49
OBSERVATION TABLE :
(1) Network : Na
SR.
NO.
V1a
Volts
I1a
mA
V2a
Volts
I2a
mA
REMARK
1 0 Port - 2 open circuited
2 0 Port - 1 short circuited
(2) Network : Nb
SR.
NO.
V1b
Volts
I1b
mA
V2b
Volts
I2b
mA
REMARK
1 0 Port - 2 open circuited
2 0 Port - 1 short circuited
(3) Network N :
SR.
NO.
V1
Volts
I1
mA
V2
Volts
I2
mA
REMARK
1 0 Port - 2 open circuited
2 0 Port - 1 short circuited
CALCULATION :
For Network Na :
I1a
g11a = ___ =
V1a I2a= 0
I1a
g12a = ___ =
I2a V1a= 0
8/14/2019 Lpw Circuit Theory 2013
46/49
V2a
g21a = ___ =
V1a I2a= 0
V2a
g22a = ___ =
I2a V1= 0
For Network Nb :
I1b
g11b = ___ =
V1b I2b= 0
I1b
g12b = ___ =
I2b V1b= 0
V2b
g21b = ___ =
V1b I2b= 0
V2b
g22b = ___ =
I2b V1b= 0
For Network N
I1
g11 = ___ =
V1 I2= 0
I1
g12 = ___ =
I2 V1= 0
8/14/2019 Lpw Circuit Theory 2013
47/49
V2
g21 = ___ =
V1 I2= 0
V2
g22 = ___ =
I2 V1= 0
Check :
(1) g11= g11a+g11b = ____________
(2) g12= g12a +g12b = ____________
(3) g21= g21a+g21b =____________
(4) g21= g21a+g21b= ____________
CONCLUSION: -
QUIZ: -
1. Will the g parameter matrix of a passive network always be symmetric?2. g-parameters matrix will not exist for which type of two port networks?3. If for any two port passive network g12is 0.6, g21= ______.4. If two networks Naand Nbare connected in parallel, g11a= 1.2 and g11b= 0.8
what will be the value of g11?
8/14/2019 Lpw Circuit Theory 2013
48/49
EXPERIMENT NO: 11 DATE :
AIM: Simulation of series RC,RL and RLC circuits with Virtual Laboratory.
PROCEDURE:
1. Open the link www.vlab.co.in
2. Click on Amrita University
3. Click on Virtual Electric Circuits.
4. Click on series RC circuits. Login through Google/Yahoo ID.
5. Click on procedure tab . Now click on simulator tab. According to procedure
prepare circuit and plot the graph.
6. Repeat step 4 and 5 for Series LC circuit and Series RLC circuit.
7. Save all the results in Network drive .
http://www.vlab.co/http://www.vlab.co/http://www.vlab.co/8/14/2019 Lpw Circuit Theory 2013
49/49
EXPERIMENT NO: 12 DATE :
AIM: Simulation of Parallel RC, RL and RLC circuits with Virtual Laboratory.
PROCEDURE:
1. Open the link www.vlab.co.in
2. Click on Amrita University
3. Click on Virtual Electric Circuits.
4. Click on Parallel RC circuits. Login through Google/Yahoo ID.
5. Click on procedure tab . Now click on simulator tab. According to procedure
prepare circuit and plot the graph.
6. Repeat step 4 and 5 for Parallel LC circuit and Parallel RLC circuit.
7. Save all the results in Network drive .
http://www.vlab.co/http://www.vlab.co/http://www.vlab.co/